The blood both in the crime scene and in the hallway was pretty fresh. If anyone has a deep wound it is unlikely they managed to bandage it or anything. There wasn't anything in the storage like first aid kits or anything like that.

[As far as Mouri knows]

This can't be something the culprit can endure stoically. There must be blood or other signs on the culprit's clothing right now, especially if the wound was deep.